1. Technical Field
One or more embodiments of the present invention relate to an X-ray inspection method and an X-ray inspection apparatus. More specifically, one or more embodiments of the present invention relate to an image pickup method for inspecting an object by using X-ray irradiation, which is a technique applicable to an X-ray inspection method and an X-ray inspection apparatus.
2. Background Art
In recent years, LSI (Large-Scale Integration) of higher degree of integration has been developed thanks to microfabrication technique of sub-microns, allowing functions which have conventionally been divided into a plurality of packages to be packed in one LSI. Because conventional QFPs (Quad Flat Packages) and PGAs (Pin Grid Arrays) can no longer accommodate the increased number of pins resulting from incorporating necessary functions in one package, LSIs of BGAs (Ball Grid Arrays) and CSPs (Chip Size Packages) in particular have been used these days. For applications that need to be microminiaturized such as mobile telephones, a BGA package is used even if the number of required pins is not so large.
While BGA and CSP packages of LSI greatly contribute to microminiaturization, soldered portions and the like are not visible from the appearance after being assembled. For this reason, when a printed board and the like having BGA and CSP packages mounted thereon is inspected, a fluoroscopic image obtained by irradiating an inspection object with an X-ray is analyzed, to determine whether or not quality is acceptable.
By way of example, Patent Document 1 (Japanese Patent Laying-Open No. 2000-46760) discloses an X-ray tomographic surface inspection apparatus capable of obtaining a sharp X-ray image by using an X-ray plane detector for detecting a transmitted X-ray.
Patent Document 2 (Japanese Patent Laying-Open No. 2003-344316) discloses a method for reconstructing an image in inclined three-dimensional X-ray CT (Computed Tomography) by arbitrarily selecting an angle of X-ray irradiation.
As shown in FIG. 21, Patent Document 3 (Japanese Patent Laying-Open No. 2003-329616) discloses an image pickup method in which a field of view (inspection object) is rotated during X-ray image pickup. While neither an X-ray source nor a detector needs to be moved during image pickup in this method, the inspection object needs to be rotated for each image pickup in order to change an image pickup angle.
As shown in FIG. 22, Patent Document 4 (Japanese Patent Laying-Open No. 2006-162335) discloses an X-ray inspection apparatus in which two-dimensional inspection is conducted based on an X-ray image obtained by a parallel X-ray detection device, and three-dimensional inspection is conducted based on an X-ray image obtained by inclined X-ray detection means, so that both inspections can be conducted at high speed. A “filtered back-projection method” is proposed as an exemplary reconstruction method. An X-ray image pickup method disclosed in Patent Document 4 is an “image pickup method using a plurality of detectors and a fixed-focal-point X-ray source,” and uses a detector arranged for picking up a transmitted image in a perpendicular direction, and a plurality of detectors for picking up transmitted images from different angles while moving on a circular trajectory. Because the X-ray source has a fixed focal point, images of one field of view are picked up from a plurality of angles by moving a substrate.
As shown in FIG. 23, Patent Document 5 (Japanese National Patent Publication No. 2004-515762) discloses an X-ray image pickup method using a scanning X-ray source and one X-ray detector fixed in position.
As shown in FIG. 24, Patent Document 6 (Japanese Patent Laying-Open No. 6-177600) discloses an X-ray image pickup method using an apparatus including a plurality of movable X-ray sources and X-ray detectors as many as the X-ray sources.
[Image Reconstruction Method of X-Ray CT]
As described above, in X-ray CT, based on measured values of an X-ray that has been transmitted through an object and then detected by an X-ray detector, at least a cross-sectional image of the object is reconstructed. Three-dimensional X-ray absorption factor distribution of the object or a part of the object is obtained. Accordingly, an arbitrary cross-sectional image of the object or a part of the object, namely, an image of a plane that crosses a light-receiving surface of the X-ray detector can be eventually reconstructed. An “analytical method” and an “iterative method” are known methods for such reconstruction. These image reconstruction methods are briefly described below.
(Description of X-Ray Projection Data)
FIG. 25 illustrates an image reconstruction method. X-ray image reconstruction is a method for measuring how much an X-ray applied externally of an inspection object has been absorbed (attenuated) by the inspection object from a plurality of different angles, to determine X-ray absorption coefficient distribution inside the inspection object.
The following description is based on the use of a so-called scanning X-ray source as an X-ray source to make a measurement.
Referring to FIG. 25, an X-ray emitted from an X-ray focal point Fa corresponding to an X-ray detector Da is transmitted through an inspection object (not shown) and reaches a pixel Pa of X-ray detector Da. When the X-ray is transmitted through the inspection object, an amount of X-ray (X-ray intensity) is attenuated by the amount corresponding to an X-ray absorption coefficient inherent in each component and the like forming the inspection object. The amount of attenuation in X-ray intensity is recorded as a pixel value of detector pixel Pa.
When the intensity of the X-ray emitted from X-ray focal point Fa is indicated as I, a path of the X-ray from X-ray focal point Fa to detector pixel Pa is indicated as t, and X-ray absorption coefficient distribution of the inspection object is indicated as f(x, y, z), intensity Ia of the X-ray that reaches detector pixel Pa is expressed in the following expression (1).Ia=I×exp {−∫f(x,y,z)dt}  (1)
Taking logarithms of both sides of this expression, the X-ray absorption coefficient distribution along path t is expressed as a line integral value in the following expression (2). A value obtained by measuring this X-ray absorption coefficient distribution by the X-ray detector is referred to as projection data. Namely, the X-ray detector detects X-ray attenuation amount distribution (or X-ray intensity distribution).∫f(x,y,z)dt=ln(I/Ia)  (2)
(Description of Analytical Method (e.g., FBP Method: Filtered Back-Projection Method))
As shown in FIG. 25, when an analytical method is used, projection data on intensity Ib of an X-ray which is emitted from a focal point Fb and reaches an X-ray detector Db arranged at a position different from the position of X-ray detector Da is detected for one inspection object (or one part of the inspection object). Such projection data is actually detected with respect to a plurality of positions for one inspection object (or one part of the inspection object), to reconstruct a cross-sectional image of the inspection object based on the projection data.
FIG. 26 shows arrangement of a field of view FOV in the inspection object shown in FIG. 25, a reconstruction pixel V as an object of operation for reconstruction in the field of view FOV, X-ray focal points Fa and Fb, and X-ray detectors Da and Db, when viewed from above. X-rays that have been transmitted through the portion of reconstruction pixel V form images on X-ray detectors Da and Db, which are enlarged in accordance with a ratio of (distance from focal point to reconstruction pixel V) to (distance from focal point to X-ray detector).
Feldkamp et al. proposed a reconstruction algorithm for three-dimensional image reconstruction based on the equation (2). This algorithm (so-called Feldkamp method) is well known as described in Non-Patent Document 1, and thus detailed description thereof will not be provided. A common filtered back-projection method is briefly described below.
Operation of determining X-ray absorption coefficient distribution f(x, y, z) from projection data by adding the projection data along path t followed by an X-ray is referred to as back projection. Because simple addition of the projection data results in blurring due to a peaked-point spread function of an image pickup system, the projection data is filtered. A high-frequency emphasizing filter such as a Shepp-Logan filter is used for this filtering. While a desirable direction of filtering is considered to be a direction perpendicular to a direction of an X-ray transmission path, the Feldkamp method conducts filtering by approximating directions of all projection data transmission paths to the same direction, thereby reconstructing an image that can be inspected.
Steps of image reconstruction in the present embodiment are described below. First, a value pa′ obtained by filtering projection data pa of detector pixel Pa of X-ray detector Da is added to a pixel value v of reconstruction pixel V. Further, a value pb′ obtained by filtering projection data pb of detector pixel Pb of X-ray detector Db is added to pixel value v of reconstruction pixel V. Consequently, v=pa′+pb′ is satisfied. By performing this back-projection operation for all or some of the X-ray detectors, final pixel value v of reconstruction pixel V is expressed in the following expression (3).v=Σ(pa′+pb′+Λ)  (3)
By performing this operation for all reconstruction pixels V in a reconstruction area (field of view) FOV, X-ray absorption coefficient distribution of the inspection object is determined, and reconstructed image data is obtained.
FIG. 27 is a flowchart illustrating process steps of such filtered back-projection method.
Referring to FIG. 27, when a process with the analytical method is started (S5002), first, projection data to be processed is selected from projection data on a plurality of picked up images (S5004). Next, the selected projection data is filtered (S5006).
Then, unprocessed reconstruction pixel V in reconstruction field of view FOV is selected (S5008), and a detector pixel corresponding to reconstruction pixel V is determined (S5010).
Then, a filtered pixel value is added to reconstruction pixel V (S5012), and it is determined whether or not addition has been done for all reconstruction pixels (S5014). If the process has not been completed for all reconstruction pixels, the process returns to step S5008, and if the process has been completed, the process proceeds to step S5016.
At step S5016, it is determined whether or not the process has been performed for all projection data. If the process has not been completed for all projection data, the process returns to step S5004. If the process has been completed for all projection data, generation of a reconstructed image ends (S5018).
(Description of Iterative Method (SART))
An iterative method is a method of reconstructing an image by regarding X-ray absorption coefficient distribution f(x, y, z) of an inspection object and projection data In (I/Ia) as an equation.
FIG. 28 is a conceptual diagram showing a concept of a process with the iterative method, when a scanning X-ray source is used. FIG. 29 is a top view of the conceptual diagram of FIG. 28.
Referring to FIGS. 28 and 29, reconstruction steps with the iterative method are described below. A vector v (with an overhead arrow→representing a vector: indicated as “v” in the following text of specification) in which pixel values of a reconstructed image are arranged in a row, and a vector p (with an overhead arrow→representing a vector: indicated as “p” in the following text of specification) in which projection data are arranged in a row are expressed in the following expressions (4) and (5).
In the following, by way of example, a pixel of an image calculated to be formed on X-ray detector Da by an X-ray from X-ray focal point Fa by assuming that reconstruction pixel V has a certain value is referred to as an intermediate projection pixel Qa, and a pixel actually observed on X-ray detector Da is referred to as detector pixel Pa. Similar pixels for X-ray detector Db are referred to as an intermediate projection pixel Qb and detector pixel Pb, respectively.
In the iterative method, for assumed reconstruction pixel vector v and its corresponding intermediate projection data vector q, iterative operation of updating assumed vector v is performed until intermediate projection data vector q can be regarded as matching with projection data of actually measured detector pixel value Pa or Pb, to determine solution v, as described below.=(v1,v2,Λ,vJ)T  (4)=(p1,p2,Λ,pI)T  (5)
Here, J indicates the number of pixels in the reconstruction area (field of view), and I indicates the number of pixels in the projection data. Further, T indicates transposition. Projection operation for associating v with p is expressed by an I×J coefficient matrix in the following expression (6).W={wij}  (6)
Here, image reconstruction with the iterative method can be formulated as a problem of solving the following linear equation (7) to determine v.=  (7)
Namely, contribution of vj to pi is defined as wij. It is noted that W indicates degree of contribution of pixel value v of a reconstructed image to pixel value p of projection data, which can be determined based on geometric positions of the X-ray focal point and the X-ray detector, and may be referred to as a detection probability or weight.
Proposed iterative methods include a method for algebraically solving an equation, and a method of considering statistical noise. A commonly used algebraic method of SART (Simultaneous Algebraic Reconstruction Technique) is described below. Details are described in Non-Patent Document 2.
In SART, first, an initial reconstructed image v0 (with an overhead arrow→representing a vector: indicated as “v0” in the following text of specification) expressed in the following expression (8) is assumed.  (8)
Initial reconstructed image v0 may be data of all 0, or data obtained from CAD (Computer Aided Design) data and the like may be assumed.
Next, intermediate projection data q0 (with an overhead arrow→representing a vector: indicated as “q0” in the following text of specification) expressed in the following expression (9) is generated by using projection operation W.=  (9)
Intermediate projection data q0 may be generated for one projection data or for a plurality of projection data. The following description is based on generation for one projection data.
Generated intermediate projection data q0 is compared with projection data p obtained from the X-ray detector. Comparison may be made with a method for calculating a difference or a method for performing division. In SART, the difference (p−q0) is calculated.
Initial reconstructed image v0 is updated. An expression (iterative equation) used for the update is expressed in the following expression (10).
                              v          j          1                =                              v            j            0                    +                                                    ∑                                  i                  =                  1                                I                            ⁢                                                                                          p                      i                                        -                                          q                      i                                                                                                  ∑                                              j                        =                        1                                            J                                        ⁢                                          w                      ij                                                                      ⁢                                  w                  ij                                                                                    ∑                                  i                  =                  1                                I                            ⁢                              w                ij                                                                        (        10        )            
Calculation time for update can be reduced by calculating the following expressions (11) and (12) in the expression (10) in advance.
                              ∑                      i            =            1                    I                ⁢                  w          ij                                    (        11        )                                          ∑                      j            =            1                    J                ⁢                  w          ij                                    (        12        )            
A reconstructed image generated by the above calculation is assigned as an initial image, and the same process is repeated several times, whereby reconstructed image data is obtained.
FIG. 30 is a flowchart illustrating a process with the iterative method.
Referring to FIG. 30, when a process with the iterative method is started (S5102), an initial reconstructed image is set (S5104). As described above, all values may be 0 in the initial reconstructed image, for example. Next, projection data to be processed is selected from among a plurality of projection data corresponding to a plurality of X-ray detector positions (S5106).
Intermediate projection data is generated. A method for generating the intermediate projection data has been described above (S5108).
Then, unprocessed reconstruction pixel V in reconstruction field of view FOV is selected (S5110).
A detector pixel corresponding to the reconstruction pixel is determined (S5112).
A value of reconstruction pixel V is updated based on an iterative equation (S5114).
Next, it is determined whether or not update has been done for all reconstruction pixels (S5116). If the process has not been completed for all reconstruction pixels, the process returns to step S5110, and if the process has been completed, the process proceeds to step S5118.
At step S5118, it is determined whether or not the process has been performed for all projection data. If the process has not been completed for all projection data, the process returns to step S5106. If the process has been completed for all projection data, the process proceeds to step S5120.
At S5120, it is determined whether or not the process has been repeated for a predetermined number of times. If the process has not been repeated, the process returns to step S5104 and is repeated by employing a current reconstruction pixel value as an initial reconstructed image. If the process has been repeated for the predetermined number of times, generation of a reconstructed image ends (S5022).
As described above, three-dimensional image of the inspection object can be reconstructed from the projection data obtained by the X-ray detector.